Question

For the resonant circuit given below, the value of the quality factor of the circuit is __________

(a) 5.6

(b) 7.1

(c) 8.912

(d) 12.6

This question was addressed to me in an interview.

This interesting question is from Problems of Series Resonance Involving Quality Factor in division Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Right choice is (b) 7.1

To explain I would say: f = \(\frac{1}{2π\sqrt{LC}} \)

= \(\frac{1}{6.28\sqrt{(10 × 10^{-6})(200 × 10^{-12})}}\)

= \(\frac{1}{6.28\sqrt{2 × 10^{-15}}}\)

= \(\frac{1}{888 × 10^{-9}}\) = 1.13 MHz

Inductive Reactance, XL = 2πfL = (6.28) (1.13 × 10^6)(10 × 10^-6)

= 70.96 Ω

∴ Q = \(\frac{X_L}{R} = \frac{70.96}{10}\) = 7.1.